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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 614874, 14 pages
http://dx.doi.org/10.1155/2013/614874
Research Article

A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation

1Mathematics Department, Faculty of Science, Taif University, P.O. Box 888, Saudi Arabia
2Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
3Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt
4Mathematics Department, Faculty of Science, Minia University, Minia, Egypt

Received 1 May 2013; Revised 2 June 2013; Accepted 4 June 2013

Academic Editor: Santanu Saha Ray

Copyright © 2013 S. M. Abo-Dahab et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to apply OHAM to solve numerically the problem of harmonic wave propagation in a nonlinear thermoelasticity under influence of rotation, thermal relaxation times, and magnetic field. The problem is solved in one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement and the temperature of the medium. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution. This optimal approach has a general meaning and can be used to get fast convergent series solutions of the different type of nonlinear fractional differential equation. The displacement and temperature are calculated for the models with the variations of the magnetic field, relaxation times, and rotation. The results obtained are displayed graphically to show the influences of the new parameters.